Eigen-reconstruction of Perturbations to the Primordial Tensor Power Spectrum

TL;DR

This paper introduces a model-independent method using eigen-analysis of the Fisher matrix to identify and constrain perturbations in the primordial tensor power spectrum from CMB B-mode data, promising high precision with future experiments.

Contribution

It develops a novel eigenmode approach to reconstruct and constrain deviations in the primordial tensor spectrum in a model-independent manner.

Findings

First three eigenmodes are constrainable within a few percent by future B-mode experiments.

Method allows iterative reconstruction of deviations from the fiducial spectrum.

Eigenmodes rank-ordered by measurability, optimizing data analysis.

Abstract

We explore the potential of the B-mode anisotropies of the Cosmic Microwave Background radiation (CMB) to constrain the shape of the primordial tensor power spectrum in a model-independent way. We expand possible perturbations to the power-law primordial tensor spectrum (predicted by the simplest single-field slow-roll inflationary models) using various sets of localized and nonlocalized basis functions and construct the Fisher matrix for their amplitudes. The eigen-analysis of the Fisher matrix would then yield a hierarchy of uncorrelated perturbation patterns (called tensor eigenmodes or TeMs) which are rank-ordered according to their measurability by data. We find that the first three TeMs are expected to be constrainable within a few percent by the next generation of B-mode experiments. We discuss how the method can be iteratively used to reconstruct the observable part of any general deviation from the fiducial power spectrum.